The figure shows a stationary wave between two fixed points $P$ and $Q$. Which point$(s)$ among $1, 2,$ and $3$ are in phase with point $X$?

$A$ string of length $1\,m$ and linear mass density $0.01\,kg/m$ is stretched to a tension of $100\,N$. When both ends of the string are fixed,the three lowest frequencies for standing waves are $f_1, f_2$,and $f_3$. When only one end of the string is fixed,the three lowest frequencies for standing waves are $n_1, n_2$,and $n_3$. Then:

$A$ travelling wave represented by $y = A \sin (\omega t - kx)$ is superimposed on another wave represented by $y = A \sin (\omega t + kx)$. The resultant is

$A$ wave $y = a \cos(kx - \omega t)$ superposes on another wave to form a stationary wave having a node at $x = 0$. What is the equation of the other wave?

The equation of a stationary wave is $y = 20 \sin(\pi x) \cos(\omega t)$,where $x$ and $y$ are in meters and $t$ is in seconds. The distance between a node and its adjacent antinode is (in $\text{ cm}$)

$A$ pulse of a wave train travels along a stretched string and reaches the fixed end of the string. It will be reflected back with